I get grossed out by the thought of dog fecal matter getting walked into the house too.
I grew up on a farm and we just always took our grubby boots off at the door, it's just kind of ingrained in me now.

I would of directly said "hey guys, I've actually decided that from now on, no one is to wear shoes in the house, it keeps the floors so much cleaner, there's a shoe rack at the door for you to use, thanks".

I personally don't see an issue with 'germs' from shoes, but I do think it keeps the floors a lot cleaner, especially carpet.

My dad always leaves his on. Always did at home as well - drove my mum mad. I don't ask him cause I know he wouldn't take them off anyway and he'd just get all sh!tty with me (yes even in my own house). If your parents aren't like my dad then just be direct. Please leave your shoes at the door thanks.

As to your parents continuing to openly ignore your requests.... that would p*ss me off something shocking. I'm going through something with my Dad atm where I have asked him to stop doing something and he continues to do it despite my DH being very direct I don't like it. I'm ready to explode

Are both your parents relatively mobile? If so slipping their shoes off shouldn't be a problem - I would just tell them straight out to take their shoes off.
We are a shoes off house but I let it slide with my dad cos he has had both his hips replaced & he has to sit down to get them on/off so I've decided it's not worth the drama 😋
My parents have a bench at the front door of their house (on a farm) just so dad can get his boots on/off.

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